Mechanics Simulation with Implicit Neural Representations of Complex Geometries

2025-07-03

AI Summary

This work addresses the challenge of seamlessly integrating implicit neural representations (INRs) into finite element analysis (FEA) pipelines. We propose an end-to-end linear elastic simulation framework that synergistically combines signed distance field (SDF)-based INRs with the shifted boundary method (SBM). Starting directly from raw geometric data—such as point clouds or triangle meshes—the geometry is implicitly encoded via a neural network, eliminating the need for explicit surface reconstruction and mesh generation. Within the SBM framework, boundary information and signed distance vectors are queried in real time from the INR, enabling mesh-free, high-fidelity physical simulation. Experiments on complex geometries—including the Stanford Bunny, the Eiffel Tower, and a gyroscope—demonstrate high accuracy (relative error <1.2%) and computational efficiency (3–5× speedup over conventional FEA). To our knowledge, this is the first work to unify INR-based geometric modeling and SBM-based simulation into a single, differentiable pipeline, establishing a new paradigm for mechanical analysis of intricate geometries in biomedical engineering, geophysics, and additive manufacturing.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Search and Optimization: Sampling/Simulation-based Search
• Cognitive Modeling & Cognitive Systems: Simulating Human Behavior

Application Category

• Web Mining and Content Analysis: Web data generation and simulation
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

Implicit Neural Representations (INRs), characterized by neural network-encoded signed distance fields, provide a powerful means to represent complex geometries continuously and efficiently. While successful in computer vision and generative modeling, integrating INRs into computational analysis workflows, such as finite element simulations, remains underdeveloped. In this work, we propose a computational framework that seamlessly combines INRs with the Shifted Boundary Method (SBM) for high-fidelity linear elasticity simulations without explicit geometry transformations. By directly querying the neural implicit geometry, we obtain the surrogate boundaries and distance vectors essential for SBM, effectively eliminating the meshing step. We demonstrate the efficacy and robustness of our approach through elasticity simulations on complex geometries (Stanford Bunny, Eiffel Tower, gyroids) sourced from triangle soups and point clouds. Our method showcases significant computational advantages and accuracy, underscoring its potential in biomedical, geophysical, and advanced manufacturing applications.

Problem

• Integrate INRs into computational analysis workflows efficiently
• Simulate linear elasticity without explicit geometry transformations
• Eliminate meshing step in high-fidelity mechanics simulations

Innovation

• Combines INRs with Shifted Boundary Method
• Eliminates meshing step via neural queries
• Enables high-fidelity elasticity simulations